Modified triplets with reduced secondary spectrum

ABSTRACT

A lens, particularly usable in a printer, consists of a middle negative component surrounded by two positive doublets. Secondary spectrum is reduced by choosing refractive materials and element focal lengths to minimize the expression (Pm - P3/V3 - Vm), where P3 and V3 are the partial dispersion and Abbe number for the negative component and Pm and Vm are the mean equivalent partial dispersion and mean equivalent Abbe number for the doublets.

U nlwu Dial? Price MODIFIED TRIPLETS WITH REDUCED SECONDARY SPECTRUM[72] Inventor: William H. Price, Rochester, N.Y.

[73] Assignee: Eastman Kodak Company, Rochester, NY.

[22] Filed: Oct. 1, 1971 [2l] Appl. No.: 185,496

[52] US. Cl ..350/227 [51] Int. Cl. ..G02b 9/26 [58] Field of Search..350/226, 227

[56] References Cited UNITED STATES PATENTS 2,279,384 4/1942 Altman..350/227 2,419,804 4/1947 Warmisham et al ..350/227 [1 1 3,694,057 [451Sept. 26, 1972 2,645,!54 7/ i953 Tronnier ..350/226 X Pn'maryExaminer-John K. Corbin Attorney-W. H. J. Kline et al.

[ ABSTRACT A lens, particularly usable in a printer, consists of amiddle negative component surrounded by two positive doublets. Secondaryspectrum is reduced by choosing refractive materials and element focallengths to minimize the expression (P... PJV, V where P, and V, are thepartial dispersion and Abbe number for the negative component and P, andV,,, are the mean equivalent partial dispersion and mean equivalent Abbenumber for the doublets.

6 Claims, 3 Drawing Figures MODIFIED TRIPLETS WITH REDUCED SECONDARYSPECTRUM CROSS REFERENCE TO RELATED APPLICATIONS BACKGROUND OF THEINVENTION 1 Field of the Invention This invention relates to lenses andin particular to modified triplets with reduced secondary spectrum whichmay be used in printers.

2. Description of the Prior Art Secondary spectrum is the inability of alens, even when corrected for longitudinal chromatic aberration, tofocus all wavelengths of light at the same point. In a design whichimproves only the monochromatic aberration corrections of anachromatized lens, secondary spectrum becomes the limiting aberration ofthe lens. In monochromatic prints, secondary spectrum tends to reducethe contrast of the final print, particularly in fine detail areas. Incolor prints, secondary spectrum is manifested as a spreading of colorfrom dark areas into adjacent light areas, a phenomenon known as colorfringing or halo.

It has been known to use modified triplets of the type having two outerpositive components surrounding a middle negative component forphotographic printing lenses. Many such lenses are well corrected formonochromatic and longitudinal chromatic aberrations. Secondary spectrumis limited in such triplets by careful selection of the materials usedin each element of the triplet. Examples of such materials may be foundin U. S. Pat. Nos. 2,645,154 and 2,645,156.

SUMMARY OF THE INVENTION provide such a printer lens with improvedsecondary spectrum correction which also is well corrected for otheraberrations such as axial and oblique spherical aberration, coma, fieldcurvature and astigmatism.

These and other objects are accomplished according to the presentinvention by a new discovery in the choice of refractive materials andelement focal lengths for such a modified triplet. More specifically, ithas been found that improved secondary spectrum correction is obtainedwhen the refractive materials and element focal lengths used in thedoublets and the refractive material used in the negative component areselected so that the expression (P P;)/( V;, is minimized, wherein P andV are the partial dispersion and Abbe number for the negative componentand P,,, and V,, are the mean equivalent partial dispersion and meanequivalent Abbe number for the doublets.

In a preferred embodiment of this invention, it has been found thatimproved secondary spectrum correction is obtained when the frontdoublet has a lower equivalent Abbe number and a higher equivalentpartial dispersion than either of its constituent elements and the reardoublet has a higher equivalent Abbe number and a lower equivalentpartial dispersion than either of its constituent elements and themiddle negative component is made of a refractive material having anAbbe number V; and a partial dispersion P, which satisfy the followinginequality:

wherein P, and V are the mean equivalent partial dispersion and meanequivalent Abbe number for the doublets.

BRIEF DESCRIPTION OF THE DRAWINGS In the detailed description of thepreferred embodiments, reference is made to the accompanying drawings,wherein:

FIG. 1 is a diagrammatic axled cross-section of a lens according to theinvention;

FIG. 2 is a graph of partial dispersion P against Abbe number V,illustrating the selection of the refractive materials and focal lengthsfor the elements in the lens of this invention; and

FIG. 3 is the spherical aberration curve for the lens of Example 1,illustrating the improved secondary spectrum correction achieved by thisinvention.

DESCRIPTION OF THE PREFERRED EMBODIMENT For all purposes of describingor claiming of the invention herein, the term lens shall be used todescribe the complete lens and not elements or components thereof. Thelong conjugate side of the lens is considered in front and is shown onthe left in FIG. 1. The term partial dispersion for a refractivematerial shall refer to the partial dispersion for the g line of mercuryand may be calculated from the following formula:

nF 0 F)/(NF C) (I) The term secondary spectrum shall be defined as thedifference between the focus for the e line of mercury and the commonfocus for the C line of hydrogen and the g line of mercury.

Primary color correction in a positive doublet is obtained by using arefractive material of low dispersion for the positive element of thedoublet and a refractive material of high dispersion for the negativeelement. Thus, a positive doublet which is well corrected for primarycolor is characterized by a large difference in Abbe number between itstwo elements. Secondary spectrum for a doublet is known to beproportional to the slope of the line on a plot of partial dispersionversus Abbe number which is defined by the parameters of the elements ofthe doublet. This slope is given by the following relationship:

slope=(P -P.,)/( a a) where the subscripts a and b refer to the twoelements of the doublet. It may be seen that the best correction ofsecondary spectrum results with equality of partial dispersion for thepositive and negative elements of the doublet. Thus a doublet, to bewell corrected for both primary sand secondary color, should haveelements with a large difference in Abbe number and equal partialdispersion.

FIG. 2 is a graph of partial dispersion, P versus Abbe number, V. Mostavailable glasses lie along or near the line K of FIG. 2, which has aslope of 0.00170. Included are the glasses represented by the points 10,12, 16 and 18 which are the glasses selected for use in the triplet ofthis invention as will be more fully described hereinafter. Because ofthis restriction of the parameters of available glasses it may be seenthat the two conditions required for a doublet to be well correctedcannot be presently met. Selection of a pair of glasses with widelydiffering Abbe numbers insures a wide difference in partial dispersion.Selection of glasses with equal partial dispersion insures near equalityof Abbe numbers.

A similar restriction holds true for the correction of a simple triplet.Primary correction again requires a large difference in dispersionbetween the positive and negative elements of the triplet. Secondaryspectrum of the triplet is proportional to the slope of the line definedon the plot of P,,- versus V by the mean parameters of the positivecomponents and the parameters of the negative element. This slope isgiven by the following relationship:

m 3)/( 3 m) It may be seen from an analysis of line K of FIG. 2 that thelarge difference in Abbe number which is required to make primary colorcorrections in a simple triplet results in a large difference in partialdispersion. In order to substantially reduce the secondary spectrum ofthe triplet, it has been found to be necessary to make some componentsof the triplet compound, with the selection of element glasses and focallengths for the compound components to be perfonned in a manner which isnow to be described.

In all embodiments of the invention, as illustrated in FIG. 1, componentI is a positive doublet consisting of a front positive biconvex element1 and a rear negative biconcave element 2. Component II consists of anegative biconcave element 3. Component III is a positive doubletconsisting of a front meniscus negative element 4, concave to the rear,and a rear positive biconvex element 5.

A doublet, consisting of two elements aand b, may be considered asequivalent to a single element of equivalent focal length I. made from ahypothetical glass having equivalent V and P values defined by thefollowing equations:

where the subscripts a and b again refer to the two element of thedoublet. The equivalent P, and V values for the hypothetical glass willlie along a straight line on the P -Vplot of FIG. 2 which is defined bythe P and V parameters of the element glasses of the doublet. Thus,component I consists of a front element 1 with parameters represented onFIG. 2 by'pointltl and a rear element 2 with parameters represented onFIG. 2 by point 12. Points 10 and 12 define a line L along which liespoint 14, representing the equivalent parameters of the hypotheticalglass of component I. Component III consists of a front element 4 withparameters represented in FIG. 2 by point 16 and a rear element 5 withparameters represented on FIG. 2 by point 18. Points 16 and 18 define aline M along which lies point 20, representing the equivalent parametersof the hypothetical glass of component III. The exact values of P and V,are determined by the selected element focal lengths for given glassesand may be positioned to the right, to the left or in between the pointsrepresenting the element glasses.

Dotted line N on FIG. 2 is defined by points 14 and 20, representing theequivalent partial dispersion and equivalent Abbe number of thehypothetical glasses found in components I and III. The mean value ofthese hypothetical parameters, represented by point 22 on line N of FIG.2, may be seen to lie substantially away from line K, which representsthe ordinarily available glasses. Secondary spectrum for the triplet isthen proportional to the slope of the line 0, defined by the meanequivalent parameters represented by point 22 and the parameters fornegative component 11. By proper selection of the mean equivalentparameters and of the parameters for negative component II of thetriplet, the slope of the PV line for the triplet may be substantiallyreduced below that available in a simple triplet, thereby insuringsubstantially improved correction of secondary spectrum. The selectionof these glasses and focal lengths will now be described in more detailwith reference to Example 1.

In all of the following examples, the lens components are numbered fromfront to rear with Roman numerals; the lens elements are numbered fromfront to rear with Arabic numerals. The element focal lengths F, theindexes of refraction N for the D line of the spectrum the Abbe numbersV, the radii of curvature R, the thicknesses T and the separations S,and the partial dispersions P are numbered by subscript from front torear. Radii of curvature having centers of curvatures to the rear of thesurface are considered positive; those with centers of curvature to thefront of the surface are considered negative. All parameters are basedupon a lens focal length of mm.

EXAMPLE 1 f/5.00 F 100mm Mag. 6.125x

Thickness or ele. N V Radius Separation mm mm PgF F S, 3.080 R. =-50.3413 1.65317 39.7 T, 4.824 0.568 R, 29.561

S, 5.846 R 249.41 4 1.65317 39.7 T,=2.546 0.568 44.1

Component Equiv. V Equiv. PgF

I 62.7 0.549 111 58.2 0.549 Mean I 60.45 0.549

As may be seen from the table of Example 1, front component I consistsof a front element 1 which is characterized by a Abbe number of 63.5 anda partial dispersion of 0.542 with an element focal length of 28.8. Rearelement 2 of front component I is characterized by a Abbe number of 64.5and a partial dispersion of 0.534 with an element focal length of 62.6.By application of fonnulas (4), (5) and (6) above, the equivalent Abbenumber and equivalent partial dispersion of front component I may becalculated and are found to be 62.7 and 0.549 respectively. Theseparameters have been plotted in FIG. 2 with the parameters of element 1defining point 10 and the parameters of element 2 defining point 12.Points 10 and 12 define a straight line L on which the parameters of theresulting equivalent hypothetical glass are represented by point 14.Analogous computations may be performed on the parameters of rearcomponent III with a resulting equivalent Abbe number and partialdispersion of 58.2 and 0.549 respectively. Rear component III isrepresented on FIG. 2 by line M with the parameters of front element 4of rear component III represented by point 16 and the parameters of rearelement 5 of rear component llI represented by point 18. The equivalentAbbe number and equivalent partial dispersion of the resultinghypothetical glass of rear component III are represented by point 20 online M. The mean equivalent Abbe number and mean equivalent partialdispersion of front and rear components l and III lies along line N,defined by points 14 and 20, and are calculated to be 60.45 and 0.549respectively.

A glass for negative component ll may now be selected using the meanequivalent Abbe number and mean equivalent partial dispersion ofcomponents I and III in such a manner as to assure proper primary colorcorrection by utilizing a large difference in Abbe number whilesimultaneously assuring good secondary color correction by minimizingthe slope of the P rV line for the triplet as described above. The glassselected for element 3 in Example I, which is the same glass as used forelement 4, results in a slope of the P V line of 0.00092, a substantialimprovement over the slope for the normal glasses which it is to beremembered is 0.00170. FIG. 3 illustrates the improved secondaryspectrum correction achieved by the design of this invention. Not onlyis the secondary spectrum reduced to 0.10 percent of the effective focallength of the lens, but it may be seen that spherical aberration hasalso been substantially reduced from available lenses. Thus both primaryand secondary color aberrations have been corrected by the selection ofglasses as described above.

Additional printer lenses which are well corrected for secondaryspectrum may be made according to this invention by following thespecification in the examples presented below. In each example, thedesign parameters for the lens are followed by the equivalent and meanAbbe numbers and equivalent and mean partial dispersions for that lensand by the calculated slope of the VP line indicating, in each example,the improved secondary correction achieved in the lenses of thisinvention.

EXAMPLE 2 174.5 F- mm Mag. -2.911x

Thlcknea or Ele. N, V, Radius Separation PgF F mm mm S, 3.712 lg--44.453 3 1.65317 39.7 '1, 4.432 0.568

S, 5.435 R, 750.18 4 1.65317 39.7 T. 2.667 0.568 -46.4

Component Equiv. V Equiv. PgF

I 62.6 0.549 111 57.6 0.549 Mean 60.1 0.549

( a m)/( V, Va) 0.00093 Example 2 is similar to Example 1, as may beseen by a comparison of the corresponding parameters. Example 2illustrates that variation in these parameters does not prevent goodsecondary spectrum correction, so long as the conditions establishedabove for selection of element glasses and focal lengths are satisfied.

EXAMPLE 3 Thickness or Ele. N,, V,, Radius Separation PgF 1- mm mm R,-31.s91 21.51700 64.5 T, 2.540 0.534 61.4

s 3.587 R. 41.187 31.65317 39.7 g T, 4.379 0.568

' s, 5.395 R.= 566.75 4 1.65317 39.7 T. 2.032 0.568 48.5

Component Equiv. V Equiv. Pg!

1 62.7 0.549 111 54.4 0.553 Mean 58.6 0.550

(P P,,.)/( V,,, V 0.0009S Example 3 is a modification of Example 2 inwhich a different glass is utilized in element 5 of component III.

Example 3 illustrates that selection of difierent glasses does notprevent good secondary spectrum correction, so long as the conditionsestablished above for selection of element glasses and focal lengths aresatisfied.

' EXAMPLE4 Thickness or R. =36.123 2 1.51700 .5 T, 3.137 0.534 -69.6R,-= 11588.

s 2.274 R. -51.346 31.65317 39.7 T, 2.640 0.568

Component Equiv.V. Equiv. PgF

' l5 1 62.8 0.552 111 57.3 0.551 Mean 60.0 0.5515

(P -P,,.)/( V,,. V )=0.00082 2o EXAMPLE 10 175.0 F 100mm Mag. 9.12011Radius Thickness or Ele. N,, V, mm Separation PgF F mm I s. 1.590 R.=38.939 31.65317 39.7 T,= 1.911 0.568

S,= 3.608 R. 214.87 41.65317 9.7 T. 1.987 0.568 40.7 R 23.630

Component Equiv. V Equiv. P3P

1 62.0 0.554 111 57.3 0.550 Mean 59.7 0.552

P3 P /V V3=0.00080 v Examples 4-8, 9 and 10 are further examples ofprinter lenses characterized by reduced secondary spectrum which weredesigned by W. H. Vangraff' eiland in accordance with the principals ofthis invention and which are disclosed and claimed in copending U. S.application Ser. No. 185,602.

EXAMPLE 1 1 r/4.5 F mm Mag. 12.000:

Thickness or Ele. ND V, Radius Separation PgF I F mm mm s. 2.056 R. 44.142 3 1.65317 39.7 T,= 2.074 0.568 5 R, I 26.483 5 1.74500 46.4 T. I6.870 0.561 23.4

Component Equiv. V Bquiv. P3P

I 62.4 p 0.550 III 57.2 0.550 Mean 59.8 0.550

( 3 111 3) EXAMPLE 12 f/ 7.09 F I 100mm Mag. I 7.25011 Thickness orfile. N, V, Radius Separation PgF F mm mm R, I 32.352 I 1.62005 .5 T I8.104 0.542 28.8

R, I -36.418 2 1.51700 64.5 T, I 4.645 0.534 53.0

S I 2.002 R. I 42.253 3 1.65317 39.7 T. I 2.976 0.568

S, I 2.220 R. 218.36 4 1.65317 39.7 T. 4.795 0.568 41.2

R, I 23.861 5 1.74500 .4 T. I 4.796 0.561 21.1

Component Equiv. V Equiv. PgF

1 62.4 0.550 III 56.5 0.550 Mean 59.5 0.550

(P; P,,.)/( V,,. V 0.00081 EXAMPLE 13 174.5 F 100mm Mag. 12.00011Thickness or Ele. N. V Radius Separation PgF F mm mm R. -32.632 21.51700 .5 T, I 2.699 0.534 57.1

S. I 2.120 R. 42.913 3 1.65317 39.7 T, 3.144 0.568

S, 3.689 R. I 351.12 4 1.65317 39.7 T. I 2.304 0.568 40.6

Component Equiv. V Equiv. PgF

I 62.3 0.553 lll 58.5).549 Mean 60.4 0.551

(P. P,,.)/( V V 0.00082 Examples 11-13 are still further examples ofprinter lenses characterized by reduced secondary spectrum which weredesigned by C. J. Melech in accordance with the principals of thisinvention and which are disclosed and claimed in copending U. S.application Ser. No. l85,630.

While this invention is described as particularly usable in a printerapplication, it will be understood that the invention can be applied tolenses designed for other applications as well and that variations andmodifications can be effected within the spirit and scope of theinvention.

lclaim:

l. A lens comprising a front positive doublet, a middle negativecomponent and a rear positive doublet, wherein the following inequalityis satisfied:

wherein P, and V, are respectively the partial dispersion and Abbenumber of said middle negative component and P and V,,, are respectivelythe mean equivalent partial dispersion and mean equivalent Abbe numberfor said front and said rear doublets.

2. A lens comprising a front positive doublet, a middle negativecomponent, and a rear positive doublet, said front and rear doubletsconsisting of one or more refractive materials such that each element insaid rear doublet has a lower Abbe number and a higher partialdispersion than either of the elements in said front doublet; the focallengths of each element in said front doublet being selected so thatsaid front doublet has a lower equivalent Abbe number and a higherequivalent partial dispersion than either of the elements in said frontdoublet; the focal lengths of each element in said rear doublet beingselected so that said rear doublet has a higher equivalent Abbe numberand a lower equivalent partial dispersion than either of the elements insaid rear doublet; and said negative component consisting of arefractive material having an Abbe number V and a partial dispersion P,which satisfy the following inequality;

wherein 1",, and V,,, are the mean equivalent partial dispersion and themean equivalent Abbe number for said front and said rear doublets.

3. A lens comprising a front positive doublet, a middle negativecomponent, and a rear positive doublet, in which the lens elements,numbered from the front side of the lens, are made of refractivematerials having substantially the following parameters, wherein V isthe Abbe number and P is the partial dispersion:-

Element V PgF 1 63.5 .542 2 64.5 .534 3 39.7 .568 4 39.7 .568 5 46.1.561

Thickness or Element N, V, Radius Separation mm mm R, I 31.787 1 1.6200563.5 T, I 10.449

R, I 35.676 2 1.51700 64.5 T, I 2.216

S, I 3.080 R, I 50.341 3 1.65317 39.7 T, I 4.824

S, I 5.846 R, I 249.41 4 1.65317 39.7 T, I 2.546

R, I 25.732 5 1.74500 46.4 T, I 5.594

wherein, from front to rear, the lens elements are numbered from 1-5,the corresponding indexes of refraction and Abbe numbers are for the Dline of the spectrum, the radii are numbered from R, to R,thethicknesses are numbered from T, to T, and the air spaces are numberedfrom S, to S,.

5. A lens having a middle negative singlet surrounded by two positivedoublets, said lens being constructed wherein, from front to rear, thelens elements are numbered from l-5, the corresponding indexes ofrefraction and Abbe numbers are for the D line of the spectrum, theradii are numbered from R, to R,, the thicknesses are numbered from T,to T, and the air spaces are numbered from S, to 5,.

6. A lens having a middle negative singlet surrounded by two positivedoublets, said lens being constructed according to the following table:

wherein, from front to rear, the lens elements are numtrum, the radiiare numbered from R, to R the bered from 1-5, the corresponding indexesof refracthicknesses are numbered from T to T, and the air tion and Abbenumbers are for the D line of the specspaces are numbered from S to 5,.

5 i t i e t

1. A lens comprising a front positive doublet, a middle negativecomponent and a rear positive doublet, wherein the following inequalityis satisfied: wherein P3 and V3 are respectively the partial dispersionand Abbe number of said middle negative component and Pm and Vm arerespectively the mean equivalent partial dispersion and mean equivalentAbbe number for said front and said rear doublets.
 2. A lens comprisinga front positive doublet, a middle negative component, and a rearpositive doublet, said front and rear doublets consisting of one or morerefractive materials such that each element in said rear doublet has alower Abbe number and a higher partial dispersion than either of theelements in said front doublet; the focal lengths of each element insaid front doublet being selected so that said front doublet has a lowerequivalent Abbe number and a higher equivalent partial dispersion thaneither of the elements in said front doublet; the focal lengths of eachelement in said rear doublet being selected so that said rear doublethas a higher equivalent Abbe number and a lower equivalent partialdispersion than either of the elements in said rear doublet; and saidnegative component consisting of a refractive mAterial having an Abbenumber V3 and a partial dispersion P3 which satisfy the followinginequality; wherein Pm and Vm are the mean equivalent partial dispersionand the mean equivalent Abbe number for said front and said reardoublets.
 3. A lens comprising a front positive doublet, a middlenegative component, and a rear positive doublet, in which the lenselements, numbered from the front side of the lens, are made ofrefractive materials having substantially the following parameters,wherein V is the Abbe number and PgF is the partial dispersion: ElementV PgF 1 63.5 .542 2 64.5 .534 3 39.7 .568 4 39.7 .568 5 46.1 .561 saidfront doublet having an equivalent Abbe number less than 63.5 and anequivalent partial dispersion greater than 0.542 and said rear doublethaving an equivalent Abbe number greater than 46.1 and an equivalentpartial dispersion less than 0.561.
 4. A lens having a middle negativesinglet surrounded by two positive doublets, said lens being constructedaccording to the following table: Thickness or Element ND VD RadiusSeparation mm mmR1 31.787 1 1.62005 63.5 T1 10.449 R2 -35.676 2 1.5170064.5 T2 2.216 R3 353.24 S1 3.080 R4 -50.341 3 1.65317 39.7 T3 4.824 R529.561 S2 5.846 R6 249.41 4 1.65317 39.7 T4 2.546 R7 25.732 5 1.7450046.4 T5 5.594 R8 -53.754 wherein, from front to rear, the lens elementsare numbered from 1-5, the corresponding indexes of refraction and Abbenumbers are for the D line of the spectrum, the radii are numbered fromR1 to R8the thicknesses are numbered from T1 to T5 and the air spacesare numbered from S1 to S2.
 5. A lens having a middle negative singletsurrounded by two positive doublets, said lens being constructedaccording to the following table: Thickness or Element ND VD RadiusSeparation mm mm R1 33.085 1 1.62005 63.5 T1 8.214 R2 -33.832 2 1.5170064.5 T2 2.535 R3 351.47 S1 3.712 R4 -44.453 3 1.65317 39.7 T3 4.432 R533.379 S2 5.435 R6 750.18 4 1.65317 39.7 T4 2.667 R7 29.064 5 1.7450046.4 T5 5.649 R8 -46.451 wherein, from front to rear, the lens elementsare numbered from 1-5, the corresponding indexes of refraction and Abbenumbers are for the D line of the spectrum, the radii are numbered fromR1 to R8, the thicknesses are numbered from T1 To T5 and the air spacesare numbered from S1 to S2.
 6. A lens having a middle negative singletsurrounded by two positive doublets, said lens being constructedaccording to the following table: Thickness or Element ND VD RadiusSeparation mm mm R1 33.747 1 1.62005 63.5 T1 8.322 R2 -31.891 2 1.5170064.5 T2 2.540 R3 4155.83 S1 3.587 R4 -41.187 3 1.65317 39.7 T3 4.379 R534.769 S2 5.395 R6 566.75 4 1.65317 39.7 T4 2.032 R7 29.892 5 1.744545.8 T5 5.639 R8 -42.892 wherein, from front to rear, the lens elementsare numbered from 1-5, the corresponding indexes of refraction and Abbenumbers are for the D line of the spectrum, the radii are numbered fromR1 to R8, the thicknesses are numbered from T1 to T5 and the air spacesare numbered from S1 to S2.